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Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 8 Jun, 2011 17:39:05 Message: 1 of 39 
Hi there, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 8 Jun, 2011 18:00:19 Message: 2 of 39 
"Aaronne" wrote in message <isoc3p$r3t$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 9 Jun, 2011 18:05:18 Message: 3 of 39 
> No, it isn't provided by MATLAB. It's a major problem for people who want to minimize a cost function for jointly estimating both images and image transformation parameters. 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 9 Jun, 2011 18:28:05 Message: 4 of 39 
"Aaronne" wrote in message <isr20u$go8$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 9 Jun, 2011 19:34:05 Message: 5 of 39 
Another thought about the transpose of affine transformations. 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 9 Jun, 2011 19:41:04 Message: 6 of 39 
"Aaronne" wrote in message <isr3bl$kj0$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 9 Jun, 2011 19:50:18 Message: 7 of 39 
"Aaronne" wrote in message <isr77d$3d6$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 9 Jun, 2011 19:59:04 Message: 8 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 9 Jun, 2011 21:41:04 Message: 9 of 39 
"Aaronne" wrote in message <isr8m8$82g$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 10 Jun, 2011 14:20:20 Message: 10 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 10 Jun, 2011 14:44:04 Message: 11 of 39 
> "Aaronne" wrote in message <isr8m8$82g$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 10 Jun, 2011 15:05:20 Message: 12 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 10 Jun, 2011 16:52:04 Message: 13 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 12 Jun, 2011 01:40:19 Message: 14 of 39 
I managed to find some old code that does both forward and transpose interpolation on 2D images. I think it will be faster than the sparse matrix construction that you're attempting. However, like I've been saying, for real speed, and especially to deal with 3D images, you're going to have to resort to C code. 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 12 Jun, 2011 02:33:02 Message: 15 of 39 
"Aaronne" wrote in message <isti3k$j9j$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 13 Jun, 2011 17:35:20 Message: 16 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 13 Jun, 2011 18:28:04 Message: 17 of 39 
"Aaronne" wrote in message <it5hoo$f9o$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 24 Aug, 2011 09:41:10 Message: 18 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 24 Aug, 2011 13:29:11 Message: 19 of 39 
"Aaronne" wrote in message <j32gvm$brh$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 30 Aug, 2011 19:31:29 Message: 20 of 39 
Sorry Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 6 Sep, 2011 14:54:28 Message: 21 of 39 
"Aaronne" wrote in message <j3jdqh$cu2$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 20 Sep, 2011 21:33:10 Message: 22 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 20 Sep, 2011 21:49:28 Message: 23 of 39 
"Aaronne" wrote in message <j5b0qm$i60$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 21 Sep, 2011 08:48:30 Message: 24 of 39 
> When you do bilinear interpolation at a point (x,y) there is a 2x2 neighbourhood of pixels around (x,y) that contribute to the interpolation. Also, interpolation can be done in separable steps in x and y . If the interpolation along x is with weights a and (1a) and the interpolation along y is with weights b and 1b, then the 4 weights associated with the 2x2 neighborhood will be 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 21 Sep, 2011 12:59:28 Message: 25 of 39 
"Aaronne" wrote in message <j5c8cu$3c5$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 21 Sep, 2011 15:53:28 Message: 26 of 39 
Very clear. Thanks. Understand now. 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 21 Sep, 2011 16:03:28 Message: 27 of 39 
Sorry about my ignorance, by thinking it over again, I feel that this line 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 21 Sep, 2011 17:55:28 Message: 28 of 39 
"Aaronne" wrote in message <j5d1sf$asi$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 21 Sep, 2011 19:47:29 Message: 29 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 21 Sep, 2011 21:48:10 Message: 30 of 39 
"Aaronne" wrote in message <j5df0h$45g$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 22 Sep, 2011 08:52:30 Message: 31 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 22 Sep, 2011 09:15:28 Message: 32 of 39 
"Aaronne" wrote in message <j5et0e$cgd$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 22 Sep, 2011 11:43:30 Message: 33 of 39 
> I can't really identify a physical meaning either, but it's pretty clear that this is the linear algebraic meaning. We can represent the contribution of a scalar x to 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 22 Sep, 2011 14:12:14 Message: 34 of 39 
"Aaronne" wrote in message <j5f712$fso$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 22 Sep, 2011 16:36:29 Message: 35 of 39 
> Recall, of course, from our past discussions that for rigid affine transformations, the transpose is approximately the inverse, and they would be identical in continuous space. That is why substituting an inverse for the transpose gives you reasonably good results in this case. 
Subject: How to get the transpose operation of the affine transformations? From: Aaronne Date: 22 Sep, 2011 21:09:29 Message: 36 of 39 
Hi Matt, 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 23 Sep, 2011 13:49:11 Message: 37 of 39 
"Aaronne" wrote in message <j5g869$3dk$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Matt J Date: 23 Sep, 2011 14:17:31 Message: 38 of 39 
"Aaronne" wrote in message <j5fo6d$qq5$1@newscl01ah.mathworks.com>... 
Subject: How to get the transpose operation of the affine transformations? From: Emroz Date: 12 Jan, 2014 18:57:06 Message: 39 of 39 
> I am planning to write my own transpose operation based on the Matlab codes you provided before. I will try to do it for 3D using Matlab and then if it is very slow I will try to make a MEX function based on C. 
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